What are the solutions to the equation x^3-5x^2+14x=0 ?

The solutions to the equation x^3-5x^2+14x=0 are x=0,x= 5/2+i(sqrt(31))/2 ,x= 5/2-i(sqrt(31))/2

Find the zeros of x^3-5x^2+14x=0

The zeros of x^3-5x^2+14x=0 are x=0,x= 5/2+i(sqrt(31))/2 ,x= 5/2-i(sqrt(31))/2

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x^{3} - 5 x^{2} + 14 x = 0

x = 0, x = \frac{5}{2} + i \frac{31}{2}, x = \frac{5}{2} - i \frac{31}{2}

Solution steps

x^{3} - 5 x^{2} + 14 x = 0

Factor

x^{3} - 5 x^{2} + 14 x : x (x^{2} - 5 x + 14)

x (x^{2} - 5 x + 14) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x = 0 or x^{2} - 5 x + 14 = 0

Solve

x^{2} - 5 x + 14 = 0 : x = \frac{5}{2} + i \frac{31}{2}, x = \frac{5}{2} - i \frac{31}{2}

The solutions are

x = 0, x = \frac{5}{2} + i \frac{31}{2}, x = \frac{5}{2} - i \frac{31}{2}

x^{3} + 3 x^{2} - 3 x - 1 = 0

x^{3} - x^{2} + 2 x = 0

(x - 5) (x^{2} - 4) = 0

x^{3} - 9 x^{2} - 81 x = - 729

x^{4} - 12 8^{\frac{13}{5}} = 0

What are the solutions to the equation x^3-5x^2+14x=0 ?
The solutions to the equation x^3-5x^2+14x=0 are x=0,x= 5/2+i(sqrt(31))/2 ,x= 5/2-i(sqrt(31))/2
Find the zeros of x^3-5x^2+14x=0
The zeros of x^3-5x^2+14x=0 are x=0,x= 5/2+i(sqrt(31))/2 ,x= 5/2-i(sqrt(31))/2